A bicycle is supported so that it is prevented from falling sideways but can move forwards or backwards; its pedals are in their highest and lowest positions. A student crouches beside the bicycle and applies a horizontal force, directed towards the back wheel, to the lower pedal.

(i) Which way does the bicycle move?

(ii) Does the chain-wheel rotate in the same or opposite sense as the rear wheel?

(iii) Which way does the lower pedal move relative to the ground?

Question

A bicycle is supported so that it is prevented from falling sideways but can move forwards or backwards; its pedals are in their highest and lowest positions. A student crouches beside the bicycle and applies a horizontal force, directed towards the back wheel, to the lower pedal.

(i) Which way does the bicycle move?

(ii) Does the chain-wheel rotate in the same or opposite sense as the rear wheel?

(iii) Which way does the lower pedal move relative to the ground?

Accepted Answer

(i) The bicycle moves in the direction of the net force (the sum of the applied backward force and the frictional force directed forwards). In usual gearings the bike moves backwards, but extremely low gearings can cause forward displacement. Because the work done is always positive, it follows that the student's hand moves backwards relative to the ground. Normally the gearing [latex] N [/latex] is greater than one, i.e. the rear wheel rotates more rapidly than the pedals. However, in the unusual case [latex] N < r /R < 1 [/latex] (where [latex] R [/latex] is the radius of the wheel and [latex] r [/latex] is the length of the pedal arm), the bicycle could move forwards despite the oppositely applied force.

(ii) The chain-wheel rotates in the same sense as the rear wheel.

(iii) Usually backwards and upwards; the superposition of (i) and (ii), but with (i) larger because of the gearing and wheel sizes.

Note. It is interesting to note that there is one position of the pedals at which an arbitrarily large force can be applied without moving the bicycle either way.

Question P.14: A bicycle is supported so that it is prevented from falling ...

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